Accelerometers let engineers measure motion when they test or monitor mechanical equipment or measure the effects of traffic on a bridge or seismic disturbances. These sensors have measurement ranges from ±1g for a MEMS-based sensor and up to ±10 kg for a large industrial sensor. The unit g stands for the free-fall acceleration on Earth; 32.17 ft/sec2 or 9.81 m/sec2. Accelerometers use a variety of sensor technologies and can provide raw, unconditioned outputs or conditioned outputs in analog or digital form, for example, 10 millivolts/g or 5 mg/least-significant bit. Some sensors' electronics will provide rms, peak, peak-to-peak and similar information. And they can measure acceleration along one, two or three axes.
Engineers routinely use accelerometers to monitor the operation of large rotating equipment such as motors, pumps, rollers and so on. Over time, shafts, bearings and couplings can wear or degrade. These changes cause equipment to vibrate more than normal often a sign of impending failure. A plot of acceleration data versus time will show changes in machinery behavior, but a plot of acceleration data in the frequency domain provides more useful information. A fast Fourier transform (FFT) does the trick and reveals the frequency components in an accelerometer's signal at a given sensor location. You should have a normal-operation baseline FFT plot to use for comparison.
Keep in mind that accelerometers have a frequency response, so check manufacturers' data sheets for a sensor's useful frequency range. Also, you must use the proper sampling rate for the bandwidth over which you plan to make measurements.
Mathematically integrating acceleration over time yields velocity data (v = gt) you can analyze with an FFT, too. But in this type of analysis, some normal vibrations often called the blade-pass frequency from fan blades, or from pump impellers or crank shafts, can dominate the frequency spectrum. A six-blade fan spun at 2,400 rpm, for example, has a 240-Hz BPF. Integrating velocity over time yields displacement (d = ½gt2) that you also can subject to an FFT, which produces a frequency versus displacement plot. This type of plot diminishes the displacement at the BPF and emphasizes the greater displacement at the motor's rotational frequency. Thus the displacement information helps engineers pinpoint characteristics of the motor and other components.
Accelerometers can have unusual applications, too. Recently, I read an article about measuring cat-purr frequencies with tiny accelerometers temporarily glued to the skin of several species of cats. Purring occurs at several frequencies between 20 and 200 Hz. I have no clue about who glued the accelerometer on a cheetah.